A layerwise multiscale analysis method for composite laminated plates

Abstract

In the two-dimensional shear deformation theories (SDT) of composite laminates, the three-dimensional plates or shells are transferred to a two-dimensional problem in the reference surface by introducing displacement fields and stress resultants along the thickness direction, the constitutive relationship is a resultant form. The multiscale analysis methods developed from SDT can not describe the periodicity along the thickness direction in composite laminated plates and shells, so it is almost impossible to accurately analyze the local stress fields surrounding the fibers based on the two scale analysis scheme. A two scale layerwise multiscale analysis method (LMAM) is established based on the Reddy’s layerwise theory (RLWT) and O(1) homogenization method for the composite laminated plates, considering the periodicity in in-plane and along the thickness direction simultaneously. The macroscopic problem of laminated plate is discretized by RLWT, while the unit cells consisted by fiber and matrix are modeling by three-dimensional finite elements. In numerical examples, the proposed LMAM is verify by using direction numerical simulation (DNS) and the O(1) homogenization method based on three-dimensional macroscopic finite elements. The unidirectional and woven composite plates are studied by the proposed LMAM; the macroscopic and microscopic stress distributions along the thickness are investigated.